Soft Frames in Soft Hilbert Spaces

In this paper, we use soft linear operators to introduce the notion of discrete frames on soft Hilbert spaces, which extends the classical notion of frames on Hilbert spaces to the context of algebraic structures on soft sets. Among other results, we show that the frame operator associated to a soft...
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Autor*in:	Osmin Ferrer [verfasserIn] Arley Sierra [verfasserIn] José Sanabria [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	soft sets soft inner product soft Hilbert space self-adjoint operator soft frame

Übergeordnetes Werk:	In: Mathematics - MDPI AG, 2013, 9(2021), 18, p 2249
Übergeordnetes Werk:	volume:9 ; year:2021 ; number:18, p 2249

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/math9182249

Katalog-ID:	DOAJ005133718

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language	English
source	In Mathematics 9(2021), 18, p 2249 volume:9 year:2021 number:18, p 2249
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topic_facet	soft sets soft inner product soft Hilbert space self-adjoint operator soft frame Mathematics
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callnumber-first	Q - Science
author	Osmin Ferrer
spellingShingle	Osmin Ferrer misc QA1-939 misc soft sets misc soft inner product misc soft Hilbert space misc self-adjoint operator misc soft frame misc Mathematics Soft Frames in Soft Hilbert Spaces
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topic_title	QA1-939 Soft Frames in Soft Hilbert Spaces soft sets soft inner product soft Hilbert space self-adjoint operator soft frame
topic	misc QA1-939 misc soft sets misc soft inner product misc soft Hilbert space misc self-adjoint operator misc soft frame misc Mathematics
topic_unstemmed	misc QA1-939 misc soft sets misc soft inner product misc soft Hilbert space misc self-adjoint operator misc soft frame misc Mathematics
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title	Soft Frames in Soft Hilbert Spaces
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title_full	Soft Frames in Soft Hilbert Spaces
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title_sort	soft frames in soft hilbert spaces
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title_auth	Soft Frames in Soft Hilbert Spaces
abstract	In this paper, we use soft linear operators to introduce the notion of discrete frames on soft Hilbert spaces, which extends the classical notion of frames on Hilbert spaces to the context of algebraic structures on soft sets. Among other results, we show that the frame operator associated to a soft discrete frame is bounded, self-adjoint, invertible and with a bounded inverse. Furthermore, we prove that every element in a soft Hilbert space satisfies the frame decomposition theorem. This theoretical framework is potentially applicable in signal processing because the frame coefficients serve to model the data packets to be transmitted in communication networks.
abstractGer	In this paper, we use soft linear operators to introduce the notion of discrete frames on soft Hilbert spaces, which extends the classical notion of frames on Hilbert spaces to the context of algebraic structures on soft sets. Among other results, we show that the frame operator associated to a soft discrete frame is bounded, self-adjoint, invertible and with a bounded inverse. Furthermore, we prove that every element in a soft Hilbert space satisfies the frame decomposition theorem. This theoretical framework is potentially applicable in signal processing because the frame coefficients serve to model the data packets to be transmitted in communication networks.
abstract_unstemmed	In this paper, we use soft linear operators to introduce the notion of discrete frames on soft Hilbert spaces, which extends the classical notion of frames on Hilbert spaces to the context of algebraic structures on soft sets. Among other results, we show that the frame operator associated to a soft discrete frame is bounded, self-adjoint, invertible and with a bounded inverse. Furthermore, we prove that every element in a soft Hilbert space satisfies the frame decomposition theorem. This theoretical framework is potentially applicable in signal processing because the frame coefficients serve to model the data packets to be transmitted in communication networks.
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title_short	Soft Frames in Soft Hilbert Spaces
url	https://doi.org/10.3390/math9182249 https://doaj.org/article/16f2664700f944698b802d1694176a14 https://www.mdpi.com/2227-7390/9/18/2249 https://doaj.org/toc/2227-7390
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